Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

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We describe a new approach to relative p-adic Hodge theory based on systematic use of
Witt vector constructions and nonarchimedean analytic geometry in the style of both …

Let L be a finite extension of Qp. We construct a (p-adic local Langlands) correspondence
attaching to any irreducible, 2-dimensional, L-representation of GQp, a unitary, admissible …

We prove the finiteness and compatibility with base change of the $(\varphi,\Gamma) $-
cohomology and the Iwasawa cohomology of arithmetic families of $(\varphi,\Gamma) …

Now in its second edition, this volume provides a uniquely detailed study of $ P $-adic
differential equations. Assuming only a graduate-level background in number theory, the text …

Using the overconvergent cohomology modules introduced by Ash–Stevens, we construct
eigenvarieties associated with reductive groups and establish some basic geometric …

The p-adic local Langlands correspondence for GL_2 (Q_p) is given by an exact functor
from unitary Banach representations of GL_2 (Q_p) to representations of the absolute Galois …

We prove the global triangulation conjecture for families of refined p-adic representations
under a mild condition. That is, for a refined family, the associated family of.';/-modules …

We show that framed deformation rings of mod p representations of the absolute Galois
group of a p-adic local field are complete intersections of expected dimension. We …